1. CONCEPT OF PHARMACOKINETICS- ONE COMPARTMENT MODEL,
DEPARTMENT OF PHARMACEUTICS

2. PHARMACOKINETICS:
PHARMACOKINETICS It is defined as the Kinetics of drug absorption, distribution, metabolism, and excretion and their relationship with pharmacological, therapeutic or toxicological response in human and animals..,

3. A typical plot represents plasma concentration-time profile..

4. KEY PARAMETERS:-
Pharmacokinetic parameters: Peak plasma concentration (Cmax), Peak time (tmax), Area under curve (AUC), t1/2(half life).
Pharmacodynamic Parameters : Minimum effective concentration, Maximum safe concentration, Onset of action, duration of action, Therapeutic range and therapeutic Index.. 

5. PHARMACOKINETIC MODELS
COMPARTMENTAL MODELS
Mammillary model
Caternary model
NON COMPARTMENTAL MODELS
PHYSIOLOGICAL MODELS

6. COMPARTMENTAL MODEL:-
COMPARTMENTAL MODEL is Hypothetical space, bound by an unspecified membrane across which drugs are transferred in and out. Depending upon whether the compartments are arranged parallel or in a series classified as Mammillary model Caternary model…

7. Mammillary model
Mammillary model consists of one (r) more periperal compartments connected to central compartment as like conection of satellite to a planet.(i.e they joined parallel to central compartment)..
Central compartment comprises plasma & highly perfused tissues. Elimination too occur from it.

8. One, Two and Three Compartment Models :

9. Model-1 cc
K10
One compartmental open model, INTRAVENOUS BOLUS
Model-2 cc
K10
K01
One compartmental open model, e.v administration

10. CC KE KE = Elimination rate constant.. ONE COMPARTMEN OPEN MODEL
IV BOLUS ADMINISTRATION KE CC
dX = Rate In – Rate Out dt
dX = - Rate Out dt
dX = - KEX dt..
KE = Elimination rate constant..
X = Amount of drug in the body..

11. dX = - KEX dt. Integrate the above eq.. ln X = ln X0 – KEt
Transfer into log form..
Log X = Log X0 - KEt /2.303
BUT X=VdC
Vd=Apparent volume of distribution(Constant)
Log C = Log C0 - KEt /2.303
C = Concentration of drug in plasma..

12. SEMILOG PLOT CARTESIAN PLOT ONE COMPARTMEN OPEN MODEL
IV BOLUS ADMINISTRATION

13. ELIMINATION RATE CONSTANT :
The decline in plasma drug concentration is only due to elimination of drug from the body, the phage is called elimination phage..
It follows 1st order elimination process..
Elimination phase characterized by parameters – elimination rate constant, elimination half life,clearence..
KE = Km + Ke

14. ELIMINATION HALF LIFE
t1/2 = / KE APPARENT VOLUME OF DISTRIBUTION For Compartment model) Vd=X/C For non compartment model Vd = X/KE.AUC(i.v bolus) Vd = X.Fo/KE.AUC(E.V adm.)

15. ClT=Clr+ClH+clothers
Clearance
The theoretical volume of body fluid containing drug from which the drug is completely removed in a given period of time..
ClT = [Rate of elimination/ Plasma drug conc.]
Cl=dx/dt / C = KEX /C
ClT=Clr+ClH+clothers

16. ORGAN CLEARANCE ER= Extraction ratio Rate of Elimination =
Rate of Presentation – Rate of exist
( Q. C in - Q. Cout)
Hepatic clearence =
ClH = ClT+Clr
ClH = QH.ERH
ER= Extraction ratio

17. CC IV INFUSION KE dX = R0- KEX dt X = Ro/KE(1-ekEt)
DRUG Ro
dX = R0- KEX dt
X = Ro/KE(1-ekEt)
C = Ro/KEVd(1-ekEt)
C = Ro/ClT(1-ekEt) CC

18. CSS
Steady state
Sope = -KE/2.303
INFUSION TIME

19. At steady state At steady state : Zero = R0 - KE Xss KE Xss = Ro
Transform into conc. Terms & rearrange the eq.
Css-c/Css = e-kEt
Transfer into log form…
log(Css-c/Css )= -KET/2.303

20. Semilog plot compute KE from infusion data upto steady -state..
Log[Css-C/Css]
Sope = -KE / 2.303
time
Semilog plot compute KE from infusion data upto steady -state..

21. INFUSION PLUS LOADING DOSE
Intravenous infusion with LOADING DOSE..As the amount of bolus dose
Falls,there is a complementary rise resulting from the infusion…

22. INFUSION PLUS LOADING DOSE
The initial bolus dose of a drug, is used to obtain desire concentration as rapidly as possible..
Xo,L = CssVd
But the loading dose simulates i.v loading dose(i.v bolus) & constant i.v infusion…
C = XoL.e-KET/Vd +Ro/KEVd[1-e-KET]

23. CC Ka KE EXTRAVASCULAR ROUTE dx/dt = KaXa-KEX
One compartment model with first order absorption
dx/dt = KaXa-KEX
Ka=first order absorption rate constant
Xa = ARA
Integrated & transform into concentration terms.., c = Ka F Xo/Ka-KE[e-KET – e-KaT ]

24. Assesment of pharmacokinetic parameters :
tmax = log(Ka/KE)/(Ka-KE)
Cmax = 0.37FXo/Vd
Elimination rate constant :
logC = log [Ka F Xo/ Vd(Ka-KE)]- KE/2.303

25. Extravascular vascular adminstration of a single dose of drug

26. Absorption rate constant Ka
It can be calculated by METHOD OF RESIDUAL
[Feathering , peeling ,stipping]
In which the plasma drug conc. Expressed by
BIEXPONENTIAL equation
c = Ka F Xo/Ka-KE[e-KEt – e-Kat ]
C = Ae-KE t – A e-Kat

27. log Cr = log A – Kat /2.303 C =True plasma conc. Cr = Residual curve..
(C – C) = Cr = Ae-Kat
C = The back extrapolated plasma conc.
C =True plasma conc.
Cr = Residual curve..
In log form the equation :
log Cr = log A – Kat /2.303

28. Biexponential cuvre = Absorption + Elimination
METHOD OF RESIDUALS
Biexponential cuvre = Absorption + Elimination

29. EXCRETION RATE CONSTANT (KE)
It can be calculated by
URINARY EXCRETION DATA
Determination of KE by
Rate of excretion method
Sigma minus method

30. Rate of excretion method

31. Transfer into log form.., log dXu/dt = log Ke Xo-KEt/2.303
Rate of excretion
Rate of urinary drug excretion(dXu/dt) α
Amount of drug in the body (X)
dXu/dt = Ke X
Ke= first order elimination rate constant..
dXu/dt = Ke Xoe-KEt
Transfer into log form..,
log dXu/dt = log Ke Xo-KEt/2.303

32. log(Xuα –Xu ) =log Xuα -KEt/2.303
Sigma minus method
The plot drawn b/n cumulative amount of drug excreted unchanged in urine & time..
dXu/dt = Ke Xo e–KEt
Integrate & rearrangement the above equation…
Xuα – Xu = Xuα e-KEt
log(Xuα –Xu ) =log Xuα -KEt/2.303

33. Sigma minus method :
log(Xuα –Xu)
Time(t)

34. REFERENCES:
Bio-Pharmaceutics and Pharmacokinetics A Treatise by D.M BRAHMANKAR; SUNIL B. JAISWAL.
Leon Shargel; et.al ; applied biopharmaceutics.
Biopharmaceutics and pharmacokinetics by Venkateswarulu

35. THANK YOU…!